Back to Graph Theory

## How to play Chomp (February 5, 2004)

__Rules__

Chomp is played on a rectangular grid, such as squares of a candy bar.
The lower left square is considered "poison". Players take turns
picking a square. With each choice, all squares above and to the right
of the picked square are no longer available --they are eaten.
The person forced to take the "poison" square loses.

*Example*: Playing on a 3x8 grid, the lower left square
(in black) is the poison square. The first player chooses the red
square of the grid and all the blue squares are eaten.

Then the second player chooses the yellow square:

The first player responds with the red square:

The second player plays the yellow square:

The first player plays the red square:

Now the second player must choose the black poison square and loses.

__Questions__

Use a piece of graph paper and try playing some games on a
variety of sizes of boards. Below are a few questions to consider
to help you think about strategies to win.

*Who has a winning strategy?* Is either player able to control
the game? If so, which player can assure he/she wins?
Hint

Answer

*Winning on a square board*:
Consider square boards (3x3, 4x4, 5x5, ...)
Can you find any positions from which you can guarantee you can win?
Hint

Answer

*Winning on a 2xn board*:
Consider boards with 2 rows (2x3, 2x4, 2x5,...)
Can you find any positions from which you can guarantee you can win?
How can you make sure that you can get to those positions?
Hint

Answer

NOTE: The 3xn case was just solved in 2002 by a high school senior,
Steven Byrnes of Lexington, MA, as part of a larger theorem.
He won the Siemens-Westinghouse Competition in Math, Science and Technology.

__Other Links*__

###### * These links are for informational
purposes only and are from sources outside MEC and Cornell University